Place Value and Roman Numerals

Date: 10/23/2001 at 20:07:16
From: James A. Lazarus
Subject: Importance of place value

What is the importance of place value in relation to the value of a 
number? For example, where the number "2" is located in a number 
changes its valuation in the number, so how does one explain the 
importance of the place value in our number system?

I have explored the realm of whole numbers, prime numbers, decimals, 
fractions, and mixed numbers, but cannot find anywhere to date, a 
cogent and readily ascertainable description or explanation of this 
phenomenon. Please explain so that I can address this problem with 
my class, as I cannot seem to describe this relation.

Date: 10/23/2001 at 23:16:26
From: Doctor Peterson
Subject: Re: Importance of place value

Hi, James.

The way to demonstrate the importance of place value is to demonstrate 
how to multiply two Roman numerals.

You will quickly find that you have to learn the same facts in 
several different guises. For example, rather than just learning that 
3 x 4 = 13, you have to learn

    III x IV = XII
    XXX x XV = CXX
    CCC x CD = MCC

Because Roman numerals have no place value, when you do the same thing 
in different digits, you have to say it different ways. With place 
value, you can continue this with numbers as large as you wish, just 
reusing the same ten symbols; Roman numerals stop at the thousands, 
because they would need two new symbols for every new decimal place 
you tack on.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/